depchi.fun: Estimates extremal dependence measures between two variables

Description Usage Arguments Details Value References See Also Examples

View source: R/depchi.fun.R

Description

This function estimates the extremal dependence coefficients χ and \bar χ by Coles et al. (1999). It also plots the functions χ(u) and \bar χ(u) against a grid of values in [0,1] to analyse the extremal dependence of two variables.

Usage

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depchi.fun(X, Y, thresval = c(0:99)/100, tit = "", indgraph = TRUE, 
	bothest = TRUE, xlegend = "topleft")

Arguments

X

Numeric vector. Values of the first variable.

Y

Numeric vector. Values of the second variable.

thresval

Numeric vector. Grid values where the functions χ(u) and \bar χ(u) are evaluated.

tit

Character string. A title for the plots.

indgraph

Logical flag. If it is TRUE, plots are carried out in individual windows. If it is FALSE, windows with 2 \times 1 plots are used.

bothest

Logical flag. If it is TRUE, two estimated coefficientes (for X given Y and for Y given X) are displayed in the same plot. Otherwise, only the coefficient for Y given X is plotted.

xlegend

Optional. Label "topleft" or"bottomright". Position where the legend on the graph will be located.

Details

The extremal dependence between two variables X and Y is the tendency for one variable to be large, given that the other one is large. The extremal dependence coefficients χ and \bar χ are defined as χ= \lim_{u \to 1} χ(u) and \bar χ(u)= 2log(P(U>u)/log P(U>u, V>u)-1, where χ(u)= P(U>u |V>u) and (U,V) are the transformed uniform marginals of the variables X and Y.

χ is on the scale [0, 1], with the set (0, 1] corresponding to asymptotic dependence, and the measure \bar χ falls within the range [-1, 1], with the set [-1, 1) corresponding to asymptotic independence. Thus, the complete pair (χ, \bar χ) is required as a summary of extremal dependence: (χ > 0, \bar χ =1) signifies asymptotic dependence, in which case the value of χ determines a measure of strength of dependence within the class; alternatively, (χ=0, \bar χ <1) signifies asymptotic independence, in which case the value of \bar χ determines the strength of dependence within this class. Full details can be found in Coles et al. (1999).

In the χ plot, the expected behaviour under independence of X and Y is also plotted.

Value

A list with elements

chiX

Estimated χ function for Y given X evaluated at the threshold grid.

chiY

Estimated χ function for X given Y evaluated at the threshold grid.

chiBX

Estimated \bar χ function for Y given X evaluated at the threshold grid.

chiBY

Estimated \bar χ function for X given Y evaluated at the threshold grid.

PX

Estimation of the probabilities P(U<thresval)

PY

Estimation of the probabilities P(V<thresval)

PXY

Estimation of the probabilities P[(U<thresval)\&(V<thresval)]

thresval

Input argument

References

Coles, S., Heffernan, J. and Tawn, J. (1999) Dependence measures for extreme value analysis. Extremes, 2, 339-365.

See Also

TestIndNH.fun, DutilleulPlot.fun, CondTest.fun

Examples

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data(BarTxTn)

aux<-depchi.fun(X=BarTxTn$Tx,Y=BarTxTn$Tn, thresval = c(0:99)/100, 
	tit = "Barcelona", xlegend = "topleft")

IndTestPP documentation built on May 29, 2017, 5:19 p.m.